Question 4 - A-Level Maths

The point $F$ is the focus of $C$.

Write down the coordinates of $F$. The point $P$ on $C$ has $y$ coordinate $q$, where $q > 0$
Show that an equation for the tangent to $C$ at $P$ is given by $$10 x - 2 q y + q ^ { 2 } = 0$$ The tangent to $C$ at $P$ intersects the directrix of $C$ at the point $A$.
The point $B$ lies on the directrix such that $P B$ is parallel to the $x$-axis.
Show that the point of intersection of the diagonals of quadrilateral $P B A F$ always lies on the $y$-axis.